About: Schläfli orthoscheme

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Schläfli orthoscheme Goto Sponge NotDistinct Permalink

An Entity of Type : owl:Thing, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon

http://dbpedia.demo.openlinksw.com/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FSchläfli_orthoscheme

In geometry, a Schläfli orthoscheme is a type of simplex. The orthoscheme is the generalization of the right triangle to simplex figures of any number of dimensions. Orthoschemes are defined by a sequence of edges that are mutually orthogonal. They were introduced by Ludwig Schläfli, who called them orthoschemes and studied their volume in Euclidean, hyperbolic, and spherical geometries. H. S. M. Coxeter later named them after Schläfli. As right triangles provide the basis for trigonometry, orthoschemes form the basis of a trigonometry of n dimensions, as developed by Schoute who called it polygonometry. J.-P. Sydler and Børge Jessen studied orthoschemes extensively in connection with Hilbert's third problem.

Attributes	Values
rdfs:label	Schläfli orthoscheme (en)
rdfs:comment	In geometry, a Schläfli orthoscheme is a type of simplex. The orthoscheme is the generalization of the right triangle to simplex figures of any number of dimensions. Orthoschemes are defined by a sequence of edges that are mutually orthogonal. They were introduced by Ludwig Schläfli, who called them orthoschemes and studied their volume in Euclidean, hyperbolic, and spherical geometries. H. S. M. Coxeter later named them after Schläfli. As right triangles provide the basis for trigonometry, orthoschemes form the basis of a trigonometry of n dimensions, as developed by Schoute who called it polygonometry. J.-P. Sydler and Børge Jessen studied orthoschemes extensively in connection with Hilbert's third problem. (en)
foaf:depiction
dcterms:subject	Polytopes
Wikipage page ID	20740340 (xsd:integer)
Wikipage revision ID	1116578228 (xsd:integer)
Link from a Wikipage to another Wikipage	Quadrirectangular tetrahedron Midpoint Birectangular tetrahedron Applied mathematics Path graph Volume Coxeter Orthogonal Pieter Hendrik Schoute Geometry Miroslav Fiedler Convex hull Convex polytope Order polytope Ludwig Schläfli Simplex Børge Jessen Tree (graph theory) Trigonometry Dissection problem Coxeter-Dynkin diagram 3-orthoscheme 4-orthoscheme 5-cell Acute angle Euclidean space Goursat tetrahedron Hilbert's third problem Hill tetrahedron Regular polytope Right angle Coxeter group Tetrahedron Hyperbolic geometry Hypercube Hyperrectangle Polytopes Chiral Edge (geometry) Jean-Pierre Sydler Triangle Dihedral angle Dilogarithm Polygonometry Circumscribed sphere Hugo Hadwiger H. S. M. Coxeter Face (geometry) Facet (geometry) Lobachevsky function Spherical geometry Right triangle Fundamental region Symmetry (mathematics)
sameAs	Schläfli orthoscheme Schläfli orthoscheme Schläfli orthoscheme Schläfli orthoscheme
dbp:wikiPageUsesTemplate	dbt:Blockquote dbt:Main dbt:R dbt:Reflist dbt:Short_description
thumbnail	wiki-commons:Special:FilePath/Triangulated_cube.svg?width=300
has abstract	In geometry, a Schläfli orthoscheme is a type of simplex. The orthoscheme is the generalization of the right triangle to simplex figures of any number of dimensions. Orthoschemes are defined by a sequence of edges that are mutually orthogonal. They were introduced by Ludwig Schläfli, who called them orthoschemes and studied their volume in Euclidean, hyperbolic, and spherical geometries. H. S. M. Coxeter later named them after Schläfli. As right triangles provide the basis for trigonometry, orthoschemes form the basis of a trigonometry of n dimensions, as developed by Schoute who called it polygonometry. J.-P. Sydler and Børge Jessen studied orthoschemes extensively in connection with Hilbert's third problem. Orthoschemes, also called path-simplices in the applied mathematics literature, are a special case of a more general class of simplices studied by Fiedler, and later rediscovered by Coxeter. These simplices are the convex hulls of trees in which all edges are mutually perpendicular. In an orthoscheme, the underlying tree is a path. In three dimensions, an orthoscheme is also called a birectangular tetrahedron (because its path makes two right angles at vertices each having two right angles) or a quadrirectangular tetrahedron (because it contains four right angles). (en)
prov:wasDerivedFrom	wikipedia-en:Schläfli_orthoscheme?oldid=1116578228&ns=0
page length (characters) of wiki page	10018 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Schläfli_orthoscheme
is Link from a Wikipage to another Wikipage of	Coxeter–Dynkin diagram Generalized trigonometry Order polytope Ludwig Schläfli Simplex Tetragonal disphenoid honeycomb 5-cell Euler brick Hill tetrahedron Tetrahedron Heronian tetrahedron Dissection into orthoschemes Simplex noise Schlafli orthoscheme Orthoscheme
is Wikipage redirect of	Schlafli orthoscheme Orthoscheme
is foaf:primaryTopic of	wikipedia-en:Schläfli_orthoscheme

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 67 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software